Automorphisms groups for $p$-cyclic covers of the affine line
| dc.creator | Lehr, Claus | |
| dc.creator | Matignon, Michel | |
| dc.date | 2003-07-02 | |
| dc.date.accessioned | 2026-07-07T04:59:22Z | |
| dc.date.available | 2026-07-07T04:59:22Z | |
| dc.description | Let $k$ be an algebraically closed field of positive characteristic $p>0$ and $C \to {\mathbb P}^1_k$ a $p$-cyclic cover of the projective line ramified in exactly one point. We are interested in the $p$-part of the full automorphism group $Aut_k C$. First we prove that these groups are exactly the extra-special $p$-groups and groups G which are subgroups of an extra-special group E such that $Z(E) \subseteq G$. The paper also describes an efficient algorithm to compute the $p$-part of $\Aut_k C$ starting from an Artin-Schreier equation for the cover $C \to {\mathbb P}^1_k$. The interest for these objects initially came from the study of the stable reduction of $p$-cyclic covers over the $p$-adics. There the covers $C \to {\mathbb P}^1_k$ naturally arise and their automorphism groups play a major role in understanding the arithmetic monodromy. Our methods rely on previous work by Stichtenoth whose approach we have adopted. | |
| dc.identifier | https://arxiv.org/abs/math/0307031 | |
| dc.identifier | http://arxiv.org/abs/math/0307031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67954 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 11G20;14H30;14Q05 | |
| dc.title | Automorphisms groups for $p$-cyclic covers of the affine line | |
| dc.type | text |